Saturday, 27 February 2016

There has been a lot of media coverage recently on the cost of attending Premier League football matches. One particular focal point was a protest by Liverpool supporters over plans to charge £77 for a ticket. In response to this protest the owners of Liverpool back-tracked and said they would keep prices pegged at current levels (where the highest price is £59). But, why should prices not go higher?

The data on Premier League attendances shows that, for the vast majority of games, stadia are full. And there is no doubt that many more would attend if they could get tickets. Such excess demand clearly means that plenty of people are willing to pay high prices. This gives a strong rationale for clubs to push prices higher and increase profit. Indeed, it is what the economic textbook says they should do.

But, the main consequence of an increase in prices is to extract surplus from supporters. Essentially supporters are pushed to the point where they are only just willing to pay to go to matches. This takes away the enjoyment of the football experience. And that is a problem because of the fairly unique nature of football.

The supporters of a club are an integral part of what that club is. This can manifest itself in many, many ways - support spurring the team on to victory, bailing out the club in hard times etc. In economic terms this means that the value of the club (and its ability to generate income) depends on its fans. Moreover, it means that fans can legitimately claim part ownership of the club. Note that this is different to most other goods. A restaurant, for example, fills up on a Saturday evening because it produces good food and not because it has a loyal fan base who cheer on the waiter.

Once we position supporters as having legitimate claim to part ownership of a club it becomes hard to justify high prices. Supporters deserve something and a ticket they can easily afford is probably a fair compensation. To say, therefore, that supporters can afford to pay high prices is not enough to justify them. And it is worth remembering that gate receipts are a relatively small proportion of revenue. At Liverpool, for instance, they are only around 20%. Much more money comes from TV rights. To squeeze every penny out of fans does not, therefore, make sense.

The protest at Liverpool showed the genuine bargaining power that fans have, if they can coordinate themselves. The owners U-turn showed good common sense.

Wednesday, 10 February 2016

A recent study by Maxwell Burton-Chelle, Claire El Mouden and Stuart West, published in the Proceedings of the National Academy of Sciences, challenges one of experimental economics most robust findings. They argue that conditional cooperation reflects subjects confusion over experimental instructions and not social preferences. So, what to make of this result?

Let me begin by providing a little background on conditional cooperation. A study by Urs Fischbacher, Simon Gachter and Ernst Fehr, published in Economics Letters 2001, looked at how people behave in a pubic good game when they get to see the contributions of others. More specifically:

They considered a setting with 4 people. Each person could contribute up to 20 tokens into a public project. Any tokens not contributed were worth, say, $1 to that person. Any tokens contributed were worth $0.40 to everyone in the group. For example, if a person keeps 5 tokens and total contributions to the group (including her 15) are 36 then she gets $5 + 0.4(35) = $19. This is the standard linear public good setting. The slight twist is to have 3 of the people choose their contribution before the 4th person. The 4th person can then condition her contribution on the contribution observed of others. The final thing to note is that a strategy method was used meaning that subjects were asked what they would do under any eventuality; that is, what would they do if the average contribution of others was 0, or 1, or 2, and so on up to 20.

Fischbacher, Gachter and Fehr found that around 50% of subjects were conditional co-operators. To a rough approximation these subjects contributed the same as the average contributed by others. So, if the average contribution of others was 15, they contributed 15, and so forth. This finding has been replicated many, many times, including a study of my own with Denise Lovett, published in Games. Moreover, the idea of conditional cooperation fits well with the more general behaviour we observe in public good games. For instance it can explain why contributions decline with repeated interaction - if 50% of people are free-riders and 50% conditional cooperators the average contribution naturally will fall over time.

The latest study in PNAS questions all this. Here's what they did: Having given subjects the same instructions as those used in the original study by Fischbacher, Gachter and Fehr. Then they wrote “Before you begin, you are going to play this game in a special case. In this special case, you will be in a group of just you and the COMPUTER; The computer will pick the decisions of the other 3 players. The computer will pick their decisions randomly and separately (so each computer player will make its own random decision); You are the only real person in the group, and only you will receive any money.”

In this special case there is absolutely no reason to contribute to the public good. If a person does contribute it merely benefits a computer, whatever that means. Yet the study found that behaviour against the computer was almost exactly the same as behaviour with people. This, it is claimed, is evidence that subjects don't understand the instructions. And conditional cooperation is an artefact of this misunderstanding. Why else would someone cooperate with a computer?

To cut to the chase, I don't buy this argument. There are several reasons. First, hundreds, if not thousands, of experimental subjects have behaved as if conditional co-operators over the years. Surely, at least some of these understood the instructions! After all, the subjects are typically students at top universities and the instructions are not particularly difficult to understand. Even so, we cannot ignore the fact that the subjects in this study did behave weirdly when playing against computers. How can we explain that?

There is a worrying circularity in the reasoning used by Burton-Chellew, El Mouden and West. In particular, they essentially claim that subjects cannot understand instructions about a public good game but can understand the bit of the instructions that tells them they are playing a computer. Well, public good games are ubiquitous in everyday life, while cooperating with a computer is an odd thing indeed. So, it seems to me much more plausible that subjects understood instructions about the public good game but did not react to the bit at the end telling them they were playing a computer.
Support for this latter interpretation is provided by the observation that behaviour against the computer was so similar to that against humans. My study with Denise Lovett and others have shown that the behaviour of conditional cooperators systematically changes with incentives. This would strongly suggest that some difference should have been observed when subjects played against computers. But, no difference was observed. The easiest explanation for this seems to be that subjects did not comprehend what it meant to play a computer.
The authors offer a counter-argument to this line of reasoning. They show that conditional cooperation correlates with 'misunderstanding of the game'. Their measure of misunderstanding is, however, open to interpretation; they asked subjects 'In the game, if a player wants to maximize his or her earnings in any one particular round, does the amount they should contribute depend on what other people in their group contribute?'. This question is carefully worded to have a unique answer - no. And I would want someone in a game theory exam to answer no. But this is not a game theory exam! Once we acknowledge that fact, this question looks more like a measure of free-riding than understanding. Indeed, the many conversations I have had with students and experimental subjects, on this kind of issue, would suggest that those answering yes or maybe are likely to understand the game better than those answering no - they just need a bit of training before sitting a game theory exam.
Clearly this latest study challenges the economist's interpretation of conditional cooperation and has to be taken seriously. But, I think the evidence is not compelling enough to ditch 15 years of accumulated evidence quite yet. Clearly, some conditional cooperation will be down to confusion. The claim that 100% is due to confusion, however, seems extreme. Hopefully, future work can narrow down the estimate.